We describe a nonlinear distortion-tolerant filter for pattern recognition that is optimum in terms of tolerance to input noise and discrimination capability. This filter was derived by minimization of the output energy that is due to the overlapping additive noise and the input scene, and the output of the filter meets the design constraints obtained from the training data set. The performance of this filter was tested with an input scene containing one of the training data sets, a nontraining true target, and a false object in the presence of overlapping additive noise and nonoverlapping background noise. We carried out Monte Carlo runs to measure the statistical performance of the filter and obtained receiver operating characteristics curves to show the detection capabilities of the filter.
© 2002 Optical Society of America
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